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    Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/36394


    Title: 有向圖的視線數
    Bar visibility number of oriented graph
    Authors: 曾煥絢
    Tseng, Huan-Hsuan
    Contributors: 張宜武
    Chang, Yi-Wu
    曾煥絢
    Tseng, Huan-Hsuan
    Keywords: 有向圖
    oriented graph
    planar
    Date: 1997
    Issue Date: 2009-09-18 18:28:17 (UTC+8)
    Abstract: 在張宜武教授的博士論文中研究到視線表示法和視線數。我們以類似的方法定義有向圖的表示法和有向圖的視線數。
    首先，我們定義有向圖的視線數為b(Ｄ) ，Ｄ為有方向性的圖，在論文中可得b(Ｄ)≦┌1/2max｛△﹢(Ｄ),△﹣(Ｄ)｝┐。另一個重要的結論為考慮一個平面有向圖Ｄ，對圖形Ｄ上所有的點v，離開點v的邊（進入的邊）是緊鄰在一起時，則可得有向圖的視線數在這圖形上是１（即 b(Ｄ)=1）。
    另外對特殊的圖形也有其不同的視線數，即對有向完全偶圖Ｄm,n ，b(Ｄm,n)≦┌1/2min｛m,n｝┐ ，而對競賽圖Ｄn ，可得b(Ｄn)≦┌n/3┐+1。
    In [2], Chang stuidied the bar visibility representations and defined bar visibility number.We defined analogously the bar visibility representation and the bar visibility number of a directed graph Ｄ.
    First we show that the bar visibility number, denoted by b(Ｄ),is at most ┌1/2max｛△﹢(Ｄ),△﹣(Ｄ)｝┐ if D is an oriented graph.And we show that b(Ｄ)=1 for the oriented planar graphs in which all outgoing (incoming) edges of any vertex v of Ｄ appear consecutively around v.For any complete bipartite digraph Ｄm,n ，b(Ｄm,n)≦┌1/2min｛m,n｝┐.For any tournament Ｄn,b(Ｄn)≦┌n/3┐+1.
    Reference: REFERENCES
    [1] J. A. Boundy and U. S. R. Murty, Graph theory with applications (1976).
    [2] Yi-Wu Chang, Bar visibility number, Ph.D. thesis, University of Illinois, 92-102, (1994).
    [3] S. Even, Graph Algorithms, Computer Science Press, Rockville, MD, (1979).
    [4] A. Lempel, S. Even, and I. Cederbaum, An algorithm for planarity testing of graphs, in Theory of Graphs (Proceedings of an International Symposium, Rome, July 1966), (P. Rosenstiehl, ed.), 215-232, Gordon and Breach, New York, (1967).
    [5] Y.-L. Lin and S.S. Skiena, Complexity aspects of visibility graphs, International journal of Computational Geometry & Applications.
    <br>[6] L. A. Melnikov, Problem at the Sixth Hungarian Colloquium on Combinatorics, Eger, (1981).
    [7] M. Schlag, F. Luccio, P. Maestrini, D. T. Lee, and C. K. Wong, A visibility problem in VLSI layout compaction, in Advances in Compution Research, Vol. 2 (F. P. Preparata, ed.), 259-282, JAI Press Inc.,Greenwich, CT, (1985).
    [8] M. Sen, S. Das, A.B. Roy, and D.B. West, Interval digraphs: An analogue of interval graphs, J. Graph Theory, Vol. 13, 189-202 (1989).
    [9] R. Tamassia and I. G. Tollis, A unified approach to visibility representations of planar graphs, Discrete and Computational Geometry, Vol. 1, 321-341 (1986).
    [10] D. B. West, Degrees and digraphs, Introduction to Graph Theory, 46-49, (1996).
    Description: 碩士
    國立政治大學
    應用數學研究所
    85751006
    86
    Source URI: http://thesis.lib.nccu.edu.tw/record/#B2002001695
    Data Type: thesis
    Appears in Collections:[Department of Mathematical Sciences] Theses

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